Math-Book-GMAT-Club

Recommendations

Info

Word Problems OverviewThe Following Points Outline a General Approach to Word Problems:1) Read the entire question carefully and get a feel for what is happening. Identify what kind of word problemyou're up against.2) Make a note of exactly what is being asked.3) Simplify the problem ‐ this is what is usually meant by 'translating the English to Math'. Draw a figure or table.Sometimes a simple illustration makes the problem much easier to approach.4) It is not always necessary to start from the first line. Invariably, you will find it easier to define what you havebeen asked for and then work backwards to get the information that is needed to obtain the answer.5) Use variables (a, b, x, y, etc.) or numbers (100 in case of percentages, any common multiple in case offractions, etc.) depending on the situation.6) Use SMART values. Think for a moment and choose the best possible value that would help you reach thesolution in the quickest possible time. DO NOT choose values that would serve only to confuse you. Also,remember to make note of what the value you selected stands for.7) Once you have the equations written down it's time to do the math! This is usually quite simple. Be very carefulso as not to make any silly mistakes in calculations.8) Lastly, after solving, cross check to see that the answer you have obtained corresponds to what was asked. Themakers of these GMAT questions love to trick students who don’t pay careful attention to what is being asked. Forexample, if the question asks you to find ‘what fraction of the remaining...’ you can be pretty sure one of theanswer choices will have a value corresponding to ‘what fraction of the total…’T ranslating Word ProblemsThese are a few common English to Math translations that will help you break down word problems. Myrecommendation is to refer to them only in the initial phases of study. With practice, decoding a word problemshould come naturally. If, on test day, you still have to try and remember what the math translations to someEnglish term is, you haven’t practiced enough!ADDITION: increased by ; more than ; combined ; together ; total of ; sum ; added to ; and ; plusSUBTRACTION: decreased by ; minus ; less ; difference between/of ; less than ; fewer than ; minus ; subtractedfromMULTIPLICATION: of ; times ; multiplied by ; product of ; increased/decreased by a factor of (this type caninvolve both addition or subtraction and multiplication!)DIVISION: per ; out of ; ratio of ; quotient of ; percent (divide by 100) ; divided by ; each‐ 33 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
EQUALS: is ; are ; was ; were ; will be ; gives ; yields ; sold for ; has ; costs ; adds up to ; the same as ; as much asVARIABLE or VALUE: a number ; how much ; how many ; whatSome T ricky Forms:'per' means 'divided by'Jack drove at a speed of 40 miles per hour OR 40 miles/hour.'a' sometimes means 'divided by'Jack bought twenty‐four eggs for $3 a dozen.'less than'In English, the ‘less than’ construction is reverse of what it is in math.For example, ‘3 less than x’ means ‘x – 3’ NOT ‘3 – x’Similarly, if the question says ‘Jack’s age is 3 less than that of Jill’, it means that Jacks age is ‘Jill’s age – 3’.The ‘how much is left’ constructionSometimes, the question will give you a total amount that is made up of a number of smaller amounts ofunspecified sizes. In this case, just assign a variable to the unknown amounts and the remaining amount will bewhat is left after deducting this named amount from the total.Consider the following:A hundred‐pound order of animal feed was filled by mixing products from Bins A, B and C, and that twice as muchwas added from Bin C as from Bin A.Let "a" stand for the amount from Bin A. Then the amount from Bin C was "2a", and the amount taken from Bin Bwas the remaining portion of the hundred pounds: 100 – a – 2a.In the following cases, order is important:‘quotient/ratio of’ constructionIf a problems says ‘the ratio of x and y’, it means ‘x divided by y’ NOT 'y divided by x'‘difference between/of’ constructionIf the problem says ‘the difference of x and y’ it means ‘x – y’Now that we have seen how it is possible, in theory, to break down word problems, lets go through a fewsimple examples to see how we can apply this knowledge.Example 1.The length of a rectangular garden is 2 meters more than its width. Express its length in terms of its width.Solution:Key words: more than (implies addition); is (implies equal to)Thus, the phrase ‘length is 2 more than width’ becomes:Length = 2 + widthExample 2.The length of a rectangular garden is 2 meters less than its width. Express its length in terms of its width.Solution:‐ 34 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Page 2 and 3: For the latest version of the GMAT
Page 4 and 5: Number TheoryDefinitionNumber Theor
Page 6 and 7: • 1 (and ‐1) are divisors of ev
Page 8 and 9: other digits: 21‐(9+8+6+9)=‐11,
Page 10 and 11: Sum of n first positive integers:Su
Page 12 and 13: Converting Decimals to Fractions•
Page 14 and 15: Operations involving the same bases
Page 16 and 17: PERCENTDefinitionA percentage is a
Page 18 and 19: Absolute ValueDefinitionThe absolut
Page 20 and 21: satisfied (‐15 is not within (‐
Page 22 and 23: FactorialsDefinitionThe factorial o
Page 24 and 25: AlgebraScopeManipulation of various
Page 26 and 27: There is a common misconception tha
Page 28 and 29: RemaindersDefinitionIf and are posi
Page 30 and 31: A. 2B. 4C. 8D. 20E. 45divided by yi
Page 32 and 33: Example #10 (hard)When positive int
Page 36 and 37: Key words: less than (implies subtr
Page 38 and 39: Distance/Speed/Time Word ProblemsWh
Page 40 and 41: In the next section we will learn h
Page 42 and 43: Time(3) = Time(1) + Time(2) ‐‐
Page 44 and 45: 3*x = 5*(x ‐ 20) ‐‐> x = 50 m
Page 46 and 47: Work Word ProblemsWhat is a ‘Work
Page 48 and 49: Example 3:Working together, printer
Page 50 and 51: Advanced Overlapping Sets ProblemsS
Page 52 and 53: the writing club. If 6 students sig
Page 54 and 55: two of the courses and 1 employee h
Page 56 and 57: Consider this problem to be an over
Page 58 and 59: Median The median of a triangle is
Page 60 and 61: • The midsegment is always parall
Page 62 and 63: Equilateral triangle all sides have
Page 64 and 65: • A right triangle where the angl
Page 66 and 67: Then the triangles ABC, CHB and CHA
Page 68 and 69: Quadrilateral A polygon with four '
Page 70 and 71: Squares A 4‐sided regular polygon
Page 72 and 73: • Area ‐ The usual way to calcu
Page 74 and 75: • A circle is the shape with the
Page 76 and 77: ChordA line that links two points o
Page 78 and 79: angle.• An inscribed angle is exa
Page 80 and 81: chords.‐ This becomes the theorem
Page 82 and 83: Coordinate GeometryDefinitionCoordi
Page 84 and 85:
As you can see, the distance formul
Page 86 and 87:
Lines in Coordinate GeometryIn Eucl
Page 88 and 89:
The equation of a straight line tha
Page 90 and 91:
Positive slopeHere, y increases as
Page 92 and 93:
A horizontal line has a slope of ze
Page 94 and 95:
Solution: We first find the slope o
Page 96 and 97:
To answer, we must find the slope o
Page 98 and 99:
Example #2Q: Find the point of inte
Page 100 and 101:
ParabolaA parabola is the graph ass
Page 102 and 103:
Standard DeviationDefinitionStandar
Page 104 and 105:
Standard deviation of is . Decrease
Page 106 and 107:
ProbabilityDefinitionA number expre
Page 108 and 109:
Therefore, the probability of getti
Page 110 and 111:
2) Reversal combinatorial approach:
Page 112 and 113:
Combinations & PermutationsDefiniti
Page 114 and 115:
1. The total number of arrangements
Page 116 and 117:
is the first termDefining Propertie
Page 118 and 119:
Solution(1) a1=8, does not tell us
Page 120 and 121:
CuboidA cube is the 3‐D generaliz
Page 122 and 123:
ConeA cone is a 3‐D object obtain
Page 124 and 125:
Volume =Surface Area w/o base =Surf
Page 126:
(2) : Sum of sides = . Not sufficie
show all

Math-Book-GMAT-Club

Create successful ePaper yourself

Delete template?

Save as template?